[WIP] Attempting to wrap randomized SVD (#41)

* Attempting to wrap randomized SVD

* Remove bad line resetting k

* Incremental progress

* Working svd_trunc

* Move SVD gauge fix to its own function

* Move randomized SVD to svd_trunc

* Fix gaugefix arguments

* Fix svd_trunc

---------

Co-authored-by: Katharine Hyatt <katharine.s.hyatt@gmail.com>

Author: kshyatt

ext/MatrixAlgebraKitAMDGPUExt/yarocsolver.jl

@@ -164,7 +164,7 @@ for (fname, elty, relty) in
 
             AMDGPU.unsafe_free!(dev_residual) 
             AMDGPU.unsafe_free!(dev_n_sweeps) 
-            return U, S, Vᴴ
+            return (S, U, Vᴴ)
         end
     end
 end

ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl

@@ -6,7 +6,7 @@ using MatrixAlgebraKit: one!, zero!, uppertriangular!, lowertriangular!
 using MatrixAlgebraKit: diagview, sign_safe
 using MatrixAlgebraKit: LQViaTransposedQR
 using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm
-import MatrixAlgebraKit: _gpu_geqrf!, _gpu_ungqr!, _gpu_unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_gesvdj!  
+import MatrixAlgebraKit: _gpu_geqrf!, _gpu_ungqr!, _gpu_unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_Xgesvdr!, _gpu_gesvdj!
 using CUDA
 using LinearAlgebra
 using LinearAlgebra: BlasFloat
@@ -30,6 +30,7 @@ _gpu_ungqr!(A::StridedCuMatrix, τ::StridedCuVector) = YACUSOLVER.ungqr!(A, τ)
 _gpu_unmqr!(side::AbstractChar, trans::AbstractChar, A::StridedCuMatrix, τ::StridedCuVector, C::StridedCuVecOrMat) = YACUSOLVER.unmqr!(side, trans, A, τ, C)
 _gpu_gesvd!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix) = YACUSOLVER.gesvd!(A, S, U, Vᴴ) 
 _gpu_Xgesvdp!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix; kwargs...) = YACUSOLVER.Xgesvdp!(A, S, U, Vᴴ; kwargs...) 
+_gpu_Xgesvdr!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix; kwargs...) = YACUSOLVER.Xgesvdr!(A, S, U, Vᴴ; kwargs...) 
 _gpu_gesvdj!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix; kwargs...) = YACUSOLVER.gesvdj!(A, S, U, Vᴴ; kwargs...)
 
 end

ext/MatrixAlgebraKitCUDAExt/yacusolver.jl

@@ -242,11 +242,70 @@ for (bname, fname, elty, relty) in
             if jobz == 'V'
                 adjoint!(Vᴴ, Ṽ)
             end
-            return U, S, Vᴴ
+            return S, U, Vᴴ
         end
     end
 end
 
+# Wrapper for randomized SVD
+function Xgesvdr!(A::StridedCuMatrix{T},
+                   S::StridedCuVector=similar(A, real(T), min(size(A)...)),
+                   U::StridedCuMatrix{T}=similar(A, T, size(A, 1), min(size(A)...)),
+                   Vᴴ::StridedCuMatrix{T}=similar(A, T, min(size(A)...), size(A, 2));
+                   k::Int=length(S),
+                   p::Int=min(size(A)...)-k-1,
+                   niters::Int=1) where {T<:BlasFloat}
+    chkstride1(A, U, S, Vᴴ)
+    m, n = size(A)
+    minmn = min(m, n)
+    jobu = length(U) == 0 ? 'N' : 'S'
+    jobv = length(Vᴴ) == 0 ? 'N' : 'S'
+    R = eltype(S)
+    k < minmn || throw(DimensionMismatch("length of S ($k) must be less than the smaller dimension of A ($minmn)"))
+    k + p < minmn || throw(DimensionMismatch("length of S ($k) plus oversampling ($p) must be less than the smaller dimension of A ($minmn)"))
+    R == real(T) ||
+        throw(ArgumentError("S does not have the matching real `eltype` of A"))
+
+    Ṽ = similar(Vᴴ, (n, n))
+    Ũ = (size(U) == (m, m)) ? U : similar(U, (m, m))
+    lda = max(1, stride(A, 2))
+    ldu = max(1, stride(Ũ, 2))
+    ldv = max(1, stride(Ṽ, 2))
+    params = CUSOLVER.CuSolverParameters()
+    dh = CUSOLVER.dense_handle()
+
+    function bufferSize()
+        out_cpu = Ref{Csize_t}(0)
+        out_gpu = Ref{Csize_t}(0)
+        CUSOLVER.cusolverDnXgesvdr_bufferSize(dh, params, jobu, jobv, m, n, k, p, niters,
+                                              T, A, lda, R, S, T, Ũ, ldu, T, Ṽ, ldv,
+                                              T, out_gpu, out_cpu)
+
+        return out_gpu[], out_cpu[]
+    end
+    CUSOLVER.with_workspaces(dh.workspace_gpu, dh.workspace_cpu,
+                             bufferSize()...) do buffer_gpu, buffer_cpu
+        return CUSOLVER.cusolverDnXgesvdr(dh, params, jobu, jobv, m, n, k, p, niters,
+                                          T, A, lda, R, S, T, Ũ, ldu, T, Ṽ, ldv,
+                                          T, buffer_gpu, sizeof(buffer_gpu),
+                                          buffer_cpu, sizeof(buffer_cpu),
+                                          dh.info)
+    end
+
+    flag = @allowscalar dh.info[1]
+    CUSOLVER.chklapackerror(BlasInt(flag))
+    if Ũ !== U && length(U) > 0
+        U .= view(Ũ, 1:m, 1:size(U, 2))
+    end
+    if length(Vᴴ) > 0
+        Vᴴ .= view(Ṽ', 1:size(Vᴴ, 1), 1:n)
+    end
+    Ũ !== U && CUDA.unsafe_free!(Ũ)
+    CUDA.unsafe_free!(Ṽ)
+
+    return S, U, Vᴴ
+end
+
 # for (jname, bname, fname, elty, relty) in
 #     ((:sygvd!, :cusolverDnSsygvd_bufferSize, :cusolverDnSsygvd, :Float32, :Float32),
 #      (:sygvd!, :cusolverDnDsygvd_bufferSize, :cusolverDnDsygvd, :Float64, :Float64),

src/MatrixAlgebraKit.jl

@@ -33,7 +33,7 @@ export LAPACK_HouseholderQR, LAPACK_HouseholderLQ,
        LAPACK_QRIteration, LAPACK_Bisection, LAPACK_MultipleRelativelyRobustRepresentations,
        LAPACK_DivideAndConquer, LAPACK_Jacobi,
        LQViaTransposedQR,
-       CUSOLVER_HouseholderQR, CUSOLVER_QRIteration, CUSOLVER_SVDPolar, CUSOLVER_Jacobi,
+       CUSOLVER_HouseholderQR, CUSOLVER_QRIteration, CUSOLVER_SVDPolar, CUSOLVER_Jacobi, CUSOLVER_Randomized,
        ROCSOLVER_HouseholderQR, ROCSOLVER_QRIteration, ROCSOLVER_Jacobi
 export truncrank, trunctol, truncabove, TruncationKeepSorted, TruncationKeepFiltered
 

src/common/gauge.jl

@@ -1,7 +1,7 @@
 function gaugefix!(V::AbstractMatrix)
     for j in axes(V, 2)
         v = view(V, :, j)
-        s = conj(sign(argmax(abs, v)))
+        s = conj(sign(_argmaxabs(v)))
         @inbounds v .*= s
     end
     return V

src/implementations/eig.jl

@@ -8,7 +8,7 @@ function copy_input(::typeof(eig_vals), A::AbstractMatrix)
 end
 copy_input(::typeof(eig_trunc), A) = copy_input(eig_full, A)
 
-function check_input(::typeof(eig_full!), A::AbstractMatrix, DV)
+function check_input(::typeof(eig_full!), A::AbstractMatrix, DV, ::AbstractAlgorithm)
     m, n = size(A)
     m == n || throw(DimensionMismatch("square input matrix expected"))
     D, V = DV
@@ -19,7 +19,7 @@ function check_input(::typeof(eig_full!), A::AbstractMatrix, DV)
     @check_scalar(V, A, complex)
     return nothing
 end
-function check_input(::typeof(eig_vals!), A::AbstractMatrix, D)
+function check_input(::typeof(eig_vals!), A::AbstractMatrix, D, ::AbstractAlgorithm)
     m, n = size(A)
     m == n || throw(DimensionMismatch("square input matrix expected"))
     @assert D isa AbstractVector
@@ -51,7 +51,7 @@ end
 # --------------
 # actual implementation
 function eig_full!(A::AbstractMatrix, DV, alg::LAPACK_EigAlgorithm)
-    check_input(eig_full!, A, DV)
+    check_input(eig_full!, A, DV, alg)
     D, V = DV
     if alg isa LAPACK_Simple
         isempty(alg.kwargs) ||
@@ -66,7 +66,7 @@ function eig_full!(A::AbstractMatrix, DV, alg::LAPACK_EigAlgorithm)
 end
 
 function eig_vals!(A::AbstractMatrix, D, alg::LAPACK_EigAlgorithm)
-    check_input(eig_vals!, A, D)
+    check_input(eig_vals!, A, D, alg)
     V = similar(A, complex(eltype(A)), (size(A, 1), 0))
     if alg isa LAPACK_Simple
         isempty(alg.kwargs) ||

src/implementations/eigh.jl

@@ -8,7 +8,7 @@ function copy_input(::typeof(eigh_vals), A::AbstractMatrix)
 end
 copy_input(::typeof(eigh_trunc), A) = copy_input(eigh_full, A)
 
-function check_input(::typeof(eigh_full!), A::AbstractMatrix, DV)
+function check_input(::typeof(eigh_full!), A::AbstractMatrix, DV, ::AbstractAlgorithm)
     m, n = size(A)
     m == n || throw(DimensionMismatch("square input matrix expected"))
     D, V = DV
@@ -19,7 +19,7 @@ function check_input(::typeof(eigh_full!), A::AbstractMatrix, DV)
     @check_scalar(V, A)
     return nothing
 end
-function check_input(::typeof(eigh_vals!), A::AbstractMatrix, D)
+function check_input(::typeof(eigh_vals!), A::AbstractMatrix, D, ::AbstractAlgorithm)
     m, n = size(A)
     @assert D isa AbstractVector
     @check_size(D, (n,))
@@ -48,7 +48,7 @@ end
 # Implementation
 # --------------
 function eigh_full!(A::AbstractMatrix, DV, alg::LAPACK_EighAlgorithm)
-    check_input(eigh_full!, A, DV)
+    check_input(eigh_full!, A, DV, alg)
     D, V = DV
     Dd = D.diag
     if alg isa LAPACK_MultipleRelativelyRobustRepresentations
@@ -70,7 +70,7 @@ function eigh_full!(A::AbstractMatrix, DV, alg::LAPACK_EighAlgorithm)
 end
 
 function eigh_vals!(A::AbstractMatrix, D, alg::LAPACK_EighAlgorithm)
-    check_input(eigh_vals!, A, D)
+    check_input(eigh_vals!, A, D, alg)
     V = similar(A, (size(A, 1), 0))
     if alg isa LAPACK_MultipleRelativelyRobustRepresentations
         YALAPACK.heevr!(A, D, V; alg.kwargs...)

src/implementations/gen_eig.jl

@@ -7,7 +7,7 @@ function copy_input(::typeof(gen_eig_vals), A::AbstractMatrix, B::AbstractMatrix
     return copy_input(gen_eig_full, A, B)
 end
 
-function check_input(::typeof(gen_eig_full!), A::AbstractMatrix, B::AbstractMatrix, WV)
+function check_input(::typeof(gen_eig_full!), A::AbstractMatrix, B::AbstractMatrix, WV, ::AbstractAlgorithm)
     ma, na = size(A)
     mb, nb = size(B)
     ma == na || throw(DimensionMismatch("square input matrix A expected"))
@@ -24,7 +24,7 @@ function check_input(::typeof(gen_eig_full!), A::AbstractMatrix, B::AbstractMatr
     @check_scalar(V, B, complex)
     return nothing
 end
-function check_input(::typeof(gen_eig_vals!), A::AbstractMatrix, B::AbstractMatrix, W)
+function check_input(::typeof(gen_eig_vals!), A::AbstractMatrix, B::AbstractMatrix, W, ::AbstractAlgorithm)
     ma, na = size(A)
     mb, nb = size(B)
     ma == na || throw(DimensionMismatch("square input matrix A expected"))
@@ -57,7 +57,7 @@ end
 # --------------
 # actual implementation
 function gen_eig_full!(A::AbstractMatrix, B::AbstractMatrix, WV, alg::LAPACK_EigAlgorithm)
-    check_input(gen_eig_full!, A, B, WV)
+    check_input(gen_eig_full!, A, B, WV, alg)
     W, V = WV
     if alg isa LAPACK_Simple
         isempty(alg.kwargs) ||
@@ -72,7 +72,7 @@ function gen_eig_full!(A::AbstractMatrix, B::AbstractMatrix, WV, alg::LAPACK_Eig
 end
 
 function gen_eig_vals!(A::AbstractMatrix, B::AbstractMatrix, W, alg::LAPACK_EigAlgorithm)
-    check_input(gen_eig_vals!, A, B, W)
+    check_input(gen_eig_vals!, A, B, W, alg)
     V = similar(A, complex(eltype(A)), (size(A, 1), 0))
     if alg isa LAPACK_Simple
         isempty(alg.kwargs) ||

src/implementations/lq.jl

@@ -10,7 +10,7 @@ function copy_input(::typeof(lq_null), A::AbstractMatrix)
     return copy!(similar(A, float(eltype(A))), A)
 end
 
-function check_input(::typeof(lq_full!), A::AbstractMatrix, LQ)
+function check_input(::typeof(lq_full!), A::AbstractMatrix, LQ, ::AbstractAlgorithm)
     m, n = size(A)
     L, Q = LQ
     @assert L isa AbstractMatrix && Q isa AbstractMatrix
@@ -20,7 +20,7 @@ function check_input(::typeof(lq_full!), A::AbstractMatrix, LQ)
     @check_scalar(Q, A)
     return nothing
 end
-function check_input(::typeof(lq_compact!), A::AbstractMatrix, LQ)
+function check_input(::typeof(lq_compact!), A::AbstractMatrix, LQ, ::AbstractAlgorithm)
     m, n = size(A)
     minmn = min(m, n)
     L, Q = LQ
@@ -31,7 +31,7 @@ function check_input(::typeof(lq_compact!), A::AbstractMatrix, LQ)
     @check_scalar(Q, A)
     return nothing
 end
-function check_input(::typeof(lq_null!), A::AbstractMatrix, Nᴴ)
+function check_input(::typeof(lq_null!), A::AbstractMatrix, Nᴴ, ::AbstractAlgorithm)
     m, n = size(A)
     minmn = min(m, n)
     @assert Nᴴ isa AbstractMatrix
@@ -66,36 +66,36 @@ end
 # --------------
 # actual implementation
 function lq_full!(A::AbstractMatrix, LQ, alg::LAPACK_HouseholderLQ)
-    check_input(lq_full!, A, LQ)
+    check_input(lq_full!, A, LQ, alg)
     L, Q = LQ
     _lapack_lq!(A, L, Q; alg.kwargs...)
     return L, Q
 end
 function lq_full!(A::AbstractMatrix, LQ, alg::LQViaTransposedQR)
-    check_input(lq_full!, A, LQ)
+    check_input(lq_full!, A, LQ, alg)
     L, Q = LQ
     lq_via_qr!(A, L, Q, alg.qr_alg)
     return L, Q
 end
 function lq_compact!(A::AbstractMatrix, LQ, alg::LAPACK_HouseholderLQ)
-    check_input(lq_compact!, A, LQ)
+    check_input(lq_compact!, A, LQ, alg)
     L, Q = LQ
     _lapack_lq!(A, L, Q; alg.kwargs...)
     return L, Q
 end
 function lq_compact!(A::AbstractMatrix, LQ, alg::LQViaTransposedQR)
-    check_input(lq_compact!, A, LQ)
+    check_input(lq_compact!, A, LQ, alg)
     L, Q = LQ
     lq_via_qr!(A, L, Q, alg.qr_alg)
     return L, Q
 end
 function lq_null!(A::AbstractMatrix, Nᴴ, alg::LAPACK_HouseholderLQ)
-    check_input(lq_null!, A, Nᴴ)
+    check_input(lq_null!, A, Nᴴ, alg)
     _lapack_lq_null!(A, Nᴴ; alg.kwargs...)
     return Nᴴ
 end
 function lq_null!(A::AbstractMatrix, Nᴴ, alg::LQViaTransposedQR)
-    check_input(lq_null!, A, Nᴴ)
+    check_input(lq_null!, A, Nᴴ, alg)
     lq_null_via_qr!(A, Nᴴ, alg.qr_alg)
     return Nᴴ
 end